Performance of Second-Order Platoon of Vehicles in Presence of Time-Delay and Noise

We study a performance measure for a network of time-delay systems based on the coupling graph and time-delay. The focus of this paper is on a time-delay second-order consensus network, where the network uncertainty is modeled by additive noise input on the update dynamics of subsystems, which has application to platoon of cars. The performance of the network is measured by the square of the $\mathcal{H}_{2}$-norm which manifests itself as the degree of the agreement among the nodes in existence of external disturbances. First, we study this performance measure as a function of time-delay and the Laplacian matrix of the network. Then, we discuss fundamental limits on the performance of the network and eventually we discuss optimal topology for the platoon of cars. Furthermore, we study a trade-off between the performance and connectivity in time-delay second-order networks. We essentially show that the performance of the network times total effective resistance is lower bounded by a constant.

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